Brutal and delicate ... a visitor looks at Matisse's The Red Room (Harmony in Red). Photograph: Leon Neal/AFP. More pictures

Great, ghastly, revolutionary and hilarious - what a strange ride From Russia is. Opening on Saturday, this long-awaited, much touted, on-and-off affair, resolved only by a last-minute change in English law, has finally arrived at London's Royal Academy. To be honest, I never altogether cared whether this exhibition came here or not. The imploring, the pleas and the goings-on about how much it mattered seemed to me a bit forced, as well as slightly absurd.

The Matisses are gorgeous, of course. The Picassos are marvellous, and the late Manet - In the Bar (Le Bouchon) - a killer. The Russian paintings are stirring and soulful and funny and, well, weird. The curator's wish-list had at its heart the French paintings acquired by Russian state museums at the time of the 1917 revolution, from the tremendous private collections of Sergei Shchukin and Ivan Morozov. Beginning with landscapes by Corot and Theodore Rousseau, via Monet and Manet, Cézanne, Gauguin, Van Gogh and right up to key paintings by Picasso and Matisse, the pitch keeps rising.

On the way, there are all sorts of oddities: a portrait of Tolstoy barefoot, dressed like a peasant; the 1905 October revolution, looking a bit like the aftermath of an Oxford May ball. These paintings remind us that this exhibition is not just a roster of familiar names and blockbuster belters. The disquieting late-summer afternoon landscape by Isaac Levitan, with its deserted farmland and a line of distant trees that close us in like a wall, is an unexpectedly claustrophobic painting - much more compelling than a nearby Monet haystack painting, which looks as though someone disguised as a compost heap is trying to sneak out of the picture and make a break for it.

Matisse's 1910 La Danse, the star of the show, burns off the wall, in the biggest room in the show. Up close, Matisse's searing orangey-red dancers are painted a duller, thinner colour than one might expect. Off-puttingly, the dancers always remind me of cavorting prawns. That aside, the execution is enjoyably rough and quick (this is the second version of the painting; the first hangs in the Museum of Modern Art in New York), making it all the more convincing. There's a real sizzle where sky and earth meet, and everything glows. Saturate a painting with too much flat colour and the eye tires of the experience: the receptors in our eyeballs turn themselves off. This is why Matisse kept the paint thin and modulated its density across the surface, keeping things nicely careless as he went. La Danse looks like an enormous theatre curtain, and is no worse for it.

But my favourite Matisse here is the Red Room (Harmony in Red), painted two years earlier, with its insistent patterned tablecloth and wallpaper, the faux-naive garden outside, the maid filling the fruit bowl. She is so quiet and oblivious to the crude blue pattern swarming over the red interior. The whole thing is audacious, mad, brutal and delicate - much riskier and more compelling than La Danse.

The collections of French art assembled by Morozov and by Shchukin, who was Matisse's and Picasso's greatest patron before the first world war, were hugely influential on the Russian artists who saw them. The paintings of Kuzma Petrov-Vodkin would be unthinkable without the example of La Danse. Actually, they're just unspeakable. Naked young boys with blurry genitalia play on a rounded green hill, much like the one in La Danse, and ride muscular red horses bareback through green waves. Matisse also got into Pyotr Miturich's portraiture, but Miturich turned the French painter into a kind of efficient and slick graphic design.

The two galleries devoted to French paintings assembled by Shchukin - who was a sort of untutored, self-taught genius, with an uncontrollable stammer and an equally uncontrollable hunger for art that saw him buy upwards of 50 Picassos before 1914 - and by the only slightly more conventional Morozov are uneven. But who wants one damn masterpiece after another? Shows like this thrive on difference, idiosyncrasy, and the occasional oddball unknown artist.

Still, it is uncomfortable to go from a hideous full-length Renoir portrait of an actress to a group of great Cézannes, to turn from a collection of Tahitian Gauguins to a repellent soft-core Maurice Denis (who advised Morozov on his collection), whose nudes look as if they were painted using Oil of Olay. And this is not the sickliest thing in the show, by any means.

Mikhail Nesterov's 1899 The Murdered Tsarevich Dmitry, youngest son of Ivan the Terrible, somehow does not evince the requisite tragedy. There is something odious about the lad: haloed, crowned and royally cloaked, hanging about in a birch wood looking insufferably smug, and quite possibly already dead. A symbol of innocent victimhood he may be, but he is equally as reminiscent of Damien in The Omen movies. Later, Boris Kustodiev's 1915 Beauty, a very ample and naked merchant's wife lounging on her patterned bed, is more alarming than the painter intends. It is hard to know where to look. She could be the prototype for Fernando Botero's small-headed, huge-bodied women.

Henri Rousseau's Muse Inspiring the Poet is a portrait of the poet Apollinaire with his partner, the painter Marie Laurencin. His muse is an altogether more substantial-looking figure than Apollinaire himself. Draped in a voluminous gown, Laurencin looks out of the canvas and raises an arm in benign greeting. We need this reassurance, before coming upon an "unprecedented parody on the eternal feminine", which is how the catalogue prepares us for Picasso's 1908, pelvis-thrusting, monstrous cubist Dryad.

There are a number of examples of the eternal feminine here, and a few of them may indeed be parodic. But none could be more eternal than Serge Diaghilev's old nanny, who sits in a distant corner of Léon Bakst's 1906 portrait of the theatrical impresario. Diaghilev looks elegant and self-composed - although Bakst noted at one point that he "posed disgustingly today ... [so] minced and pestered me to make him look more refined and handsome that I nearly attacked him with my brushes".

Boris Grigoriev's 1916 portrait of the theatre director Vsevolod Meyerhold shows him in two guises: top-hatted and tailed, miming a sort of white-gloved cha-cha; and dressed oriental-fashion, as a mysterious archer in slippers. It is tragic to look at this image, bearing in mind that in 1940, Meyerhold, a major influence on Russian revolutionary theatre and film-making, was accused of murdering his wife (though this was probably a pretext). Interrogated, humiliated and horribly tortured, he was eventually shot on Stalin's orders.

In its way, From Russia does attempt to deal with the larger history, not just of art and of revolutions, whether formal, ideological, or political. Events overtake everything and everyone, even artworks. Take Natalia Goncharova's 1910 Pillars of Salt, in which not only Lot's wife, but the entire Lot household have been solidified as menhir-like salt people. It is almost impossible now to take this, or Picasso's Dryad, entirely seriously. Whatever horror there was, whatever atavistic primordial essence Picasso was trying to get back to, has long gone, replaced by an irritating inner voice whispering to me that these have become cartoons.

While Picasso drew inspiration from Oceanic and African art, Goncharova and a number of her contemporaries formed a group who looked to folk art, peasant carvings and street signs - as well as to the French artists then appearing in Russian collections. In the winter of 1910 they took part in a Moscow show called Jack of Diamonds, one of the high points of which was Ivan Mashkov's Self Portrait with Pyotr Konchalovsky. This very large canvas shows the artist and his friend as musclemen, sitting in their salon in their underpants and socks, coffee on the table, dumb-bells on the floor, sheet music for popular Spanish dances on the piano. This is brilliant, and purposely funny. One beefcake clutches a violin. Books on Giotto and Cézanne teeter off the shelf. In fact, the painting is a sort of spoof on Cézanne's early Girl at the Piano, which Morozov had bought from Vollard in 1908.

No matter how variable this exhibition might be, it is worth braving the crowds. The hectic, calamitous Kandinsky, Pavel Filonov's weirdly fractured figures in his 1914-15 The German War, Tatlin's mock-up for his immense tower, and Alexandra Exter's gentle takes on cubism are all, in their way, valuable. And at the end, we come to Kazimir Malevich. A red, off-kilter square on a white ground, from 1915, staring back, irreducible, electric. Then three canvases from 1923: a black cross, a black square, a black circle. They have a finality and authority that artists everywhere are still trying to deal with. These come from Russia.

From Russia, with no love lost The row behind the show

It was meant to cause a stir, but when the Royal Academy began planning From Russia two years ago, it couldn't have known quite how much of a stir there would be.

Russia's four biggest museums - the Pushkin and the Tretyakov in Moscow, the Hermitage and the Russian Museum in St Petersburg - agreed to lend the RA more than 120 masterpieces. But in December 2007, just weeks before the paintings were due to arrive, Russia's state culture agency, Roskultura, cancelled the exhibition. The ownership of some French works, seized by Lenin in 1917, is disputed, and Roskultura feared the original owners' descendants could lay claim to them on British soil.

The decision came at a sensitive time. Relations between Britain and Russia had grown frosty in the wake of Russia's refusal to allow the extradition of Andrei Lugovoi, the man suspected of killing the former spy Alexander Litvinenko in London in 2006. Britain subsequently expelled four diplomats from the Russian embassy, and Russia is now demanding that two of its branches of the British Council be closed. But a breakthrough came earlier this month: culture secretary James Purnell rushed through legislation to protect foreign-owned assets from seizure. The exhibition was back on.

For those claiming to be the paintings' rightful owners, it was not such good news. Pierre Konowaloff and André-Marc Delocque-Fourcaud, descendants of Russian tsarist-era art collectors, have accepted an invitation to the exhibition but say they deserve financial compensation for their ancestors' loss.Laura Barnett

· From Russia: French and Russian Master Paintings 1870-1925 from Moscow and St Petersburg is at the Royal Academy of Arts, London, from Saturday until April 18. Details: 0870 848 8484